A Characterization of Black’s Voting Rule

• Authors: Walter Bossert and Salvador Barberà.
• BSE Working Paper: 1515 | October 25
• Keywords: Social choice correspondences , Black’s voting rule , Borda count , strong Condorcet winners
• JEL codes: D71, D72, D63

In his 1958 classic, The Theory of Committees and Elections, Duncan Black proposed the following lexicographic rule: for any set of feasible alternatives, and any pro- file of voters’ goodness relations, choose the strong Condorcet winner if it exists, and select the set of Borda winners otherwise. We provide what we think is the first axiomatic characterization of this rule. We do so through the intermediary study of the generalized social welfare functions that underlie the rule’s choices, and the use of axioms that emphasize what is common and what is different in the spirit of the amply debated proposals made by these two 18th-century authors.